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Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness

  • Embrechts, Paul
  • Neslehová, Johanna
  • Wüthrich, Mario V.
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    Mainly due to new capital adequacy standards for banking and insurance, an increased interest exists in the aggregation properties of risk measures like Value-at-Risk (VaR). We show how VaR can change from sub to superadditivity depending on the properties of the underlying model. Mainly, the switch from a finite to an infinite mean model gives a completely different asymptotic behaviour. Our main result proves a conjecture made in Barbe et al. [Barbe, P., Fougères, A.L., Genest, C., 2006. On the tail behavior of sums of dependent risks. ASTIN Bull. 36(2), 361-374].

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    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 44 (2009)
    Issue (Month): 2 (April)
    Pages: 164-169

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    Handle: RePEc:eee:insuma:v:44:y:2009:i:2:p:164-169
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

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    1. Muller, Alfred, 1997. "Stop-loss order for portfolios of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 219-223, December.
    2. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    3. Jon Danielsson & Bjørn N. Jorgensen & Sarma Mandira & Gennady Samorodnitsky & C. G. de Vries, 2005. "Subadditivity re–examined: the case for value-at-risk," LSE Research Online Documents on Economics 24668, London School of Economics and Political Science, LSE Library.
    4. Alink, Stan & Lowe, Matthias & V. Wuthrich, Mario, 2004. "Diversification of aggregate dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 77-95, August.
    5. J. Dhaene & R. J. A. Laeven & S. Vanduffel & G. Darkiewicz & M. J. Goovaerts, 2008. "Can a Coherent Risk Measure Be Too Subadditive?," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 365-386.
    6. Wei, Gang & Hu, Taizhong, 2002. "Supermodular dependence ordering on a class of multivariate copulas," Statistics & Probability Letters, Elsevier, vol. 57(4), pages 375-385, May.
    7. Marco Moscadelli, 2004. "The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee," Temi di discussione (Economic working papers) 517, Bank of Italy, Economic Research and International Relations Area.
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